arXiv subjects

Nelson Callegari Jr.

Publications and source records attributed to Nelson Callegari Jr..

5 recordsLinked to original sources

arXiv2026

Revisiting the dynamics of the Prometheus-Pandora system

This study revisits the dynamics of Prometheus and Pandora. The analysis focuses on their current orbits and considers mutual perturbations and the non-spherical shape of Saturn. Numerical integrations of the full equations of motion were performed in the context of the N-body problem using a dense set of initial conditions. Spectral analysis of these orbits, together with an interpretation of the dynamical maps, revealed several resonance domains of various orders between Prometheus and Pandora, including the 121:118 resonance domain. Resolving the secular equations for eccentricity and inclination revealed the absence of a forced component in both cases. The period associated with the precession rate, $\Delta\varpi$, corresponds to the anti-alignment period. Chaos was quantified by analysing the diffusion of independent frequencies, which indicates dynamics governed by weak chaos. Minor perturbations caused by the Janus-Epimetheus pair on the orbits of Prometheus and Pandora were also considered. Finally, we investigated the dynamical history of the Prometheus Pandora system, accounting for Pandora's migration due to tidal interactions with Saturn. This revealed several past cross-resonances with a low probability of capture, as well as a scenario in which the Prometheus-Pandora pair exhibited a co-orbital configuration.

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arXiv2023

The orbit of Aegaeon and the 7:6 Mimas-Aegaeon resonance

Aegaeon (S/2008 S 1) is the last satellite discovered by the Cassini spacecraft at the end of the 2000s. Like the satellites Methone and Anthe, it is involved in mean motion resonance with the mid-sized Mimas. In this work, we give a detailed analysis of the current orbit of Aegaeon identifying the resonant, secular and long-term perturbations due to Mimas and the oblateness of Saturn, and the effects of Tethys. For this task, we perform thousands of numerical simulations of full equations of motion of ensembles of small bodies representing clones of Aegaeon. We have mapped the domain of the 7:6 Mimas-Aegaeon resonance in the phase space of the semi-major axis and eccentricity. It displays a large area dominated by regular motions associated with the 7:6 corotation resonance surrounded by chaotic layers. Aegaeon is currently located very close to the periodic orbit of the resonance, which extends up to eccentricities $\sim0.025$ centered at semi-major axis $\sim168,028$ km. We show that the current orbit of Aegaeon has an important forced component in eccentricity due to the 7:6 resonance. The orbital inclination of Aegaeon has a non-negligible forced value due to long-term perturbations of Mimas. These two forced modes explain the complex perturbed orbit of Aegaeon without requiring the co-existence of multiple resonances.

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arXiv2022

The current orbit of Methone (S/2004 S 1)

The Cassini spacecraft discovered many close-in small satellites in Saturnian system, and several of them exhibit exotic orbital states due to interactions with Mimas and the oblateness of the planet. This work is devoted to Methone, which is currently involved in a 15:14 Mean-Motion Resonance with Mimas. We give an in deep study the current orbit of Methone by analyzing and identifying the short, resonant and long-term gravitational perturbations on its orbit. In addition, we perform numerical integrations of full equations of motion of ensembles of close-in small bodies orbiting the non-central field of Saturn. Spectral analyses of the orbits and interpretation of them in dynamical maps allow us to describe the orbit and the dynamics of Methone in view of resonant and long-term dynamics. We show that the current geometric orbit of Methone is aligned with Mimas' due to a forced resonant component in eccentricity, leading to simultaneous oscillations of several critical angles of the expanded disturbing function. Thus, we explain the simultaneous oscillations of four critical arguments associated to the resonance. The mapping of the Mimas-Methone resonance shows that the domains of the 15:14 Mimas-Methone resonance are dominated by regular motions associated to the Corotation resonance located at eccentricities lower than $\sim 0.015$ and osculating semi-major axis in the interval 194,660-194,730 km. Methone is currently located deeply within this site.

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arXiv2016

Coupled orbital and spin evolution of the CoRoT-7 two-planet system using a Maxwell viscoelastic rheology

We investigate the orbital and rotational evolution of the CoRoT-7 two-planet system, assuming that the innermost planet behaves like a Maxwell body. We numerically resolve the coupled differential equations governing the instantaneous deformation of the inner planet together with the orbital motion of the system. We show that, depending on the relaxation time for the deformation of the planet, the orbital evolution has two distinct behaviours: for relaxation times shorter than the orbital period, we reproduce the results from classic tidal theories, for which the eccentricity is always damped. However, for longer relaxation times, the eccentricity of the inner orbit is secularly excited and can grow to high values. This mechanism provides an explanation for the present high eccentricity observed for CoRoT-7 b, as well as for other close-in super-Earths in multiple planetary systems.

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arXiv2009

Long-term dynamics of Methone, Anthe and Pallene

We numerically investigate the long-term dynamics of the Saturn's small satellites Methone (S/2004 S1), Anthe (S/2007 S4) and Pallene (S/2004 S2). In our numerical integrations, these satellites are disturbed by non-spherical shape of Saturn and the six nearest regular satellites. The stability of the small bodies is studied here by analyzing long-term evolution of their orbital elements. We show that long-term evolution of Pallene is dictated by a quasi secular resonance involving the ascending nodes ($Ω$) and longitudes of pericentric distances ($\varpi$) of Mimas (subscript 1) and Pallene (subscript 2), which critical argument is $\varpi_2-\varpi_1-Ω_1+Ω_2$. Long-term orbital evolution of Methone and Anthe are probably chaotic since: i) their orbits randomly cross the orbit of Mimas in time scales of thousands years); ii) numerical simulations involving both small satellites are strongly affected by small changes in the initial conditions.

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